<p> plotG, discrete poly </p>

1bcf4f2b-c1df-4615-9cd1-1cc63089cadd 84 4 5 decimal

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Исходные данные

ρ 900 kg m 3^/ * :

dтр 0.012 m * :

L1 8 m * :

hydraulic resistance ζф 1.5 :

0.47" diameter

Δтр 5105 -^* m * :

Qmax 30104 -^* m 3^s / * :

viscosity ν 30106 -^* m 2^s / * :

ζф dтр * 0.018 m *

dQ 0.05 104 -^* m 3^s / * :

res Q1 0 : V1 0 : Re1 0 : λ1 64 : Δp1 0 : j 1 : Q1 Qmax ≤ Q j 1 el Q1 : V j 1 el V1 : Re j 1 el Re1 : λ j 1 el λ1 : Δp j 1 el Δp1 : Q1 Q1 dQ + : V1 4 Q1 * π dтр 2^* / : Re1 V1 dтр * ν / : λ1 Re1 2320 ≤ 105 Re1 / Re1 10000 ≤ 0.3164 Re1 (0.25^/ 0.1 Δтр dтр / 68 Re1 / + (0.254^* if if 11 line : Δp1 ρ V1 2^* λ1 L1 * ζф dтр * + (* 2 dтр * / : j j 1 + : 111 line while Q V Re λ Δp 15 mat 81 line :

governs meshing of system

'Q' increment 3600 0.1 104 -^* (* m 3^'hr / * 0.036 m 3^'hr / *

'Q' max 360030104 -^* (* m 3^'hr / * 10.8 m 3^'hr / *

Q V Re λ Δp 15 mat res eval :

collected/simplified
in program  ... λ1 L1 dтр / * ρ V1 2^* 2 / * ζф ρ V1 2^* 2 / * +

Q Max V Max Re Max λ Max Δp Max 51 mat 0.003 m 3^s / * 26.526 m s / * 10610.33 64 7.122 106^* kg m s 2^* / * 51 mat

Q Min V Min Re Min λ Min Δp Min 51 mat 000 0.0315 051 mat

i 1 Q rows range :

i rows 601

Q i Q augment : V i V augment : Re i Re augment : λ i λ augment : Δp i 0.00001 Δp * augment : 51 sys

New i Δp 2 col kg m s 2^* / / augment eval :

Convert Pa ► bar

from slope/intercept x Q 5106 -^* x * : x V 0.0442 x * 0.0442 - : x Re 17.6839 x * 17.6839 - : 31 sys

x spline Δp 1 col Δp 2 col x cinterp :

U 450 :

U spline 42.2811

Q x Q 2 1 sys V x V 2 1 sys Δp U U spline + 20 red 1 5 mat 2 1 sys

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Re x Re 2 1 sys λ λ . 10 red plot 2 1 sys

λ 1642 5.9376 3 2.9688 4 1.9792 5 1.4844 6 1.1875 7 0.9896 8 0.8482 82 mat

Re 102 17.6839 3 35.3678 4 53.0516 5 70.7355 6 88.4194 7 106.1033 8 123.7872 82 mat

λ ... as a function, i.e: interpolation

select 123571119100300600110 mat :

data select List collects index list ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 41 line :

select the support points XY λ select List :

XY 1642 5.9376 3 2.9688 5 1.4844 7 0.9896 11 0.5938 19 0.3299 100 0.06 300 0.0371 600 0.0315 102 mat

length Thiele j XY rows : 10

Thiele on length of support points 'j'
algo style ... Optimiz => NONE K X x Cfr N j 1 + el K j 1 + el : c j el N j el : a j el K j el : jj j 1 - (0 range c jj el a jj 1 + el : a jj el K jj el x X jj el - c jj el / + : 21 line for a 1 el 51 line :

The continued fraction ... Optimiz => NONE K X x Cfr K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el / + / + / + / + / + / + / + / + / +

X XY 1 col : Y XY 2 col : 12 mat

4 appVersion 0.98.6179.21440 ≡

Thiele table of inverse differences ... Carlos i 1 Y rows range Table i 1 el Y i el : for j 2 Y rows range i j Y rows range Table i j el X j 1 - el X i el - Table j 1 - j 1 - el Table i j 1 - el - / : cont j : 21 line break try for for i 1 cont range K i el Table i i el : for 31 line

K K 12 round vectorize :

Exponential treshold 15 K 64 0.0172228529 - 64.31995752311 - 12.1820464683 0.319957523111 32696548885517.6 - 0.000000000005 13780389781458.8 - 0.000000000002 47921543046420.4 101 mat

... NUMERIC ...

Expand to View/Export as required Table 11 mat

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

x λ K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el / + / + / + / + / + / + / + / + / + :

x c 11 x ≤ cases :

support XY . 14 red plot :

U 1.125 :

U λ 47.5009

x λ x c * support U U λ + 40 red 1 5 mat 3 1 sys

Δp ... as a function, i.e: interpolation

<p> plotG, discrete poly </p>

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Low High step x fnct inc U Low High step range : i 1 U rows range f i el U i el fnct : for U f augment 31 line :

XY New 27601 range 12 range el :

X XY 1 col : Y XY 2 col : 12 mat vx New 1 col : vy New 2 col : 12 mat new vx vy . 9 black plotG : 31 line

x φ 1 x x 2^31 mat :

Cholesky companion solver j 1 x φ length range i 1 X length range M i j el X i el φ j el : for for Φ M transpose M * : d M transpose Y * : 12 mat b Φ 1 -^eval d * : 31 line

M transpose M * not commutative ≡

b 0.021517 - 0.018638 0.000167 31 mat

M transpose Y * not commutative ≡

x Δp b 1 x x 2^31 mat * :

1 Δp 601 Δp 21 mat 0.0027 - 71.5627 21 mat

0 71.8279 21 mat

new x Δp 2 1 sys

Q V Re 10601 0.003 22 mat 10601 26.526 22 mat 10601 10610.33 22 mat 23 mat

160121 mat 0 0.003 21 mat Intercept 5106 -^* -

160121 mat 0 26.526 21 mat Intercept 0.0442 -

160121 mat 0 0.003 21 mat Slope 5106 -^*

160121 mat 0 26.526 21 mat Slope 0.0442

x Q 5106 -^* x * (:

x V 0.0442 x * 0.0442 - (:

160121 mat 0 10610.33 21 mat Intercept 17.6839 -

160121 mat 0 10610.33 21 mat Slope 17.6839

x Re 17.6839 x * 17.6839 - (:

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

part New 10 Decimate :

Part part . 10 black plot :

Part x Δp 2 1 sys